How do you find the roots, real and imaginary, of $y=-23x^2+5x+2$ using the quadratic formula?

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How do you find the roots, real and imaginary, of $y=-23x^2+5x+2$ using the quadratic formula?

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Answer 1 · 2016-05-20T02:59:56

$(5 +- sqrt209)/46$

Explanation:

Use the improved quadratic formula (Socratic Search)
$y = -23x^2 + 5x + 2 = 0$
$D = d^2 = b^2 - 4ac = 25 + 184 = 209$ --> $d = +- sqrt209$
There are 2 real roots:
$x = -b/(2a) +- d/(2a) = -5/-46 +- sqrt209/-46 =$
$= (5 +- sqrt209)/46$

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How do you find the roots, real and imaginary, of $y=-23x^2+5x+2$ using the quadratic formula?

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How do you find the roots, real and imaginary, of $y=-23x^2+5x+2$ using the quadratic formula?